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For the Swedish male height example, σ = 3 inches, n = 48, x-bar = 71 inches, and CL = 95% so z(0.025) = 1.96. What is the resulting 95% confidence interval for the population mean height?
A(70.15, 71.85)
B(68.00, 74.00)
C(71.00, 71.85)
D(65.00, 77.00)
Answer & Solution
Correct answer: A. (70.15, 71.85)
1. EBM = z(σ/sqrt(n)) = (1.96)(3/sqrt(48)) ≈ (1.96)(0.4330) ≈ 0.8487.
2. Lower bound: 71 - 0.8487 ≈ 70.15.
3. Upper bound: 71 + 0.8487 ≈ 71.85.
4. Option C applies the error bound to only the upper side of x-bar, which is not how a two-sided confidence interval is built.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.1 A Single Population Mean using the Normal Distribution_
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